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arXiv · 2012.10451

RG flow of integrable $\mathcal{E}$-models

Falk Hassler
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Abstract

We compute the one- and two-loop RG flow of integrable $σ$-models with Poisson-Lie symmetry. They are characterised by a twist function with $2N$ simple poles/zeros and a double pole at infinity. Hence, they capture many of the known integrable deformations in a unified framework, which has a geometric interpretation in terms of surface defects in a 4D Chern-Simons theory. We find that these models are one-loop renormalisable and present a very simple expression for the flow of the twist function. At two loops only models with $N$=1 are renormalisable. Applied to the $λ$-deformation on a semisimple group manifold, our results reproduce the $β$-functions in the literature.

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Falk Hassler. 2020-12-18. RG flow of integrable $\mathcal{E}$-models. https://doi.org/10.1016/j.physletb.2021.136367

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